Heteroatoms (B, N, S) doped quantum dots as potential drug delivery system for isoniazid: insight from DFT, NCI, and QTAIM

Toxicity in drug includes target toxicity, immune hypersensitivity and off target toxicity. Recently, advances in nanotechnology in the areas of drug delivery have help reduce toxicity and enhance drug solubility and deliver drugs to target sites more efficiently. In this study, we present a novel heteroatom functionalized quantum dot (QD-NBC and QD-NBS) as an effective drug delivery system for isoniazid. The said QD has been computationally modeled to assess its effectiveness in delivering isoniazid to desired target. Density functional theory (DFT) calculations were performed on the QD at the B3LYP/6−311+G(d, p) level to assess its stability through the natural bond orbital (NBO) calculations, and frontier molecular orbital (FMO) before and after interaction with isoniazid drug to understand any change in molecular behavior of the surface. Appropriate intermolecular interactions between the QD and the drug were computed through the Quantum theory of atoms in molecules (QTAIM) and Non-covalent interaction to assess the various binding mechanism and possible interactions resulting to the effective delivery of the drug target. To understand and accurately appraise the binding energy of adsorption, DFT calculations were performed with different functionals (B3LYP, CAM-B3LYP, PBEPBE, GD3BJ & WB97XD/6−311+G (d, p)). The results from DFT calculations point the functionalized QDs to be stable with appreciable energy gap suitable for delivery purposes. The adsorption energy of the drug target with the QD is in the range of −24.73 to 33.75 kcal/mol which indicates substantial interaction of the drug with the QD surface. This absorption energy is comparable with several reported literature and thus prompt the suitability of the surface for isoniazid delivery.


Introduction
Drug delivery discusses strategies involved in transporting a combination of drugs to their intended destination to achieve the desired treatment effect. Recent advances in nanotechnology of drug delivery systems have impacted the medical field, these drug Gaussian16 and GaussView6.0.16 package [20,21]. Natural bond orbital (NBO) 7.0 program was used to study inter molecular charge transfer as well as the stability of the surfaces [22]. The geometry optimization was achieved using the Becke's three parameter exchange-functional combined with corrected correlation Lee, Yang and Parr functional (B3LYP) methods using 6− 311+G(d,p) basis set. The optimized structures are in local minima on their potential energy surfaces, which are recognized by the absence of imaginary frequency in the Hessian matrix. The nature of interaction between the drug molecule and surface were attained using the quantum theory of atom in molecules (QTAIM) with the aid of multiwfn Analyzer [23]. Non-covalent interactions were achieved using RDG scattered, while the visualization was done using VMD [24], this was done to achieve intermolecular and van der Waals interactions, which aid in understanding the mechanism of isoniazid drug delivery by the doped quantum dot surface. In achieving the doped quantum dots surface, quantum dot surface which comprises of 36 carbon atoms (QD-CCC), Heteroatoms (B, N, S) replace carbon atoms in the central ring of the surface. To determine the adsorption energy, quantum dots and isoniazid were optimized with same basis set and was calculated using; Adsorption energy = ΔE ads = E (Drug/quantum dot) − (E (Drug) + E (Quantum dot) ) The dispersion correction and induction moments interactions are the main constituents of the attractive vdW interaction at long ranges. Although, the overlap and exchange interactions also contribute at the short range repulsive regions [25]. The conventional pure-GGA and hybrid-GGA are the most popular DFT functionals which gives point by point clarification of both the ionic and the covalent interactions, but such methods cannot predict vdW interactions precisely, because they failed in calculating dispersion forces [26]. In which Becke 88 GGA functional is used for exchange and the LYP functional for non-local correlation. There are different approaches to account for dispersion interactions in DFT [27], from which DFT-GD3BJ dispersion correction method is a robust and widely used method in which dispersion interaction implemented as an add-on to standard Kohn-Sham density functional. The Becke 3-parameter Lee-Yang-Parr functional with dispersion correction B3LYP-GD3BJ, the long-range dispersion correction functional by the Head-Gordon group (ωB97XD), The new hybrid exchange correlation functional CAM-B3LYP which combines the hybrid qualities and the long range correction. The hybrid-exchange correlation (PBE0) all with the 6− 311G (d) basis set were employed to study the interactions between the drug molecule and the doped graphene surface. Selected functional are expected to predict accurately weak interactions.

Before drug delivery
Frontier molecular orbital is a theory that helps explain the use of HOMO-LUMO energy analysis within the system under investigation. HOMO-LUMO (Highest occupied and lowest unoccupied molecular orbitals) represents the ability to donate or receive electrons respectively to any surfaces and play an important role in its electrical and optical properties and chemical reactions and are represented in negative form (see Eqs. (2) and (3)). Large and small HOMO-LUMO spaces mean molecules that are "heavy" and "soft" chemically. If not, it was found that complex chemical regeneration is also related to its "hard" molecules with a lower HOMO-LUMO gap. HUMO/LUMO assists in calculating energy gap, chemical strength, chemical hardness, chemical softness and electrophilicity.
Hence, the global reactivity descriptors could be computed using Eqs. (4), (5), (6), and (7) as suggested in literatures [28,29]. where μ, χ, η, ω, and S are the chemical potential, electronegativity, chemical hardness, electrophilicity, and chemical softness respectively calculated as reported in Table 1 while the orbital density distributions are shown in Figure 2. In the isolated state, it is reported that QD-NBS is the most reactive surface due to it low energy gap and this makes it less stable this could be as a result of the doped atom which are highly electronegative (N and S). In contrast QD-CCC is less reactive but more stable due to it high energy gap, this is as a result of the electronegativity difference between C-C bond. When values for chemical hardness (η) are small it indicates great reactivity which is due to lower needed energy to promote an electron from the HOMO to LOMO orbitals. Obtained values for (η) ranges within 2.000-1.137 eV this suggest good surface reactivity. The polarizability of a compound which is determined by the value of chemical softness, this implies that the larger the value for chemical softness the higher the polarizability. From this work the values for chemical softness followed a trend of; QD-NBS 0.439 > QD-NBC 0.358 > QD-CCC 0.220. This describes that QD-NBS is the most polarized when compared to other surfaces. It is evident that QD-NBS is the most reactive and is strongly polarized. However, quantum dot surfaces exhibits potential for drug delivery due to the reactivity and stability level.

After drug delivery
The HOMO-LUMO energy gap analyses of the interacted surfaces are presented in Table 2 while the various interaction modes between the quantum dots and the drug are displayed in Figure 3. From Table 2, QD-NBS was reported to be the most reactive due to its low energy gap in the isolated state. After interaction, it was observed that the interaction between sulfur and oxygen from the drug and the quantum dot NBS exhibited the same result as earlier reported. S-O interaction on QD-NBS has the lowest energy gap and makes it more reactive compared to other interactions. It is evident that sulfur reacts with nearly all other elements and gives a better

Natural bond orbital (NBO) analysis
Natural bond orbitals (NBO) provide details on how a compound's donor and acceptor orbitals interact. The Lewis orbital type describes the bonding NBOs, whereas the non-Lewis orbital type describes the antibonding NBOs [30]. In NBO analysis, all potential interactions between filled and empty NBOs are taken into account, and their energy relevance is determined using second order perturbation theory [31]. Eq. (8) estimates the stabilization energy (E2) links with electron delocalization among Lewis (filled) and non-Lewis (unfilled) for each electron donor (i) and electron acceptor (j).

Table 3
Second order perturbation theory analysis of the most interacting NBO'S of the studied quantum dots using B3LYP/6-311'+G (d) functional. Compound 5240.23 0.60 1.590 The degree of interaction between the donor and acceptor orbital is determined by the stabilization energy E (2) , the larger the stabilization energy the stronger the interaction [32]. Stabilization energy for the most interacting donor and acceptor orbitals in this study is presented in Table 3. Bonding to anti-bonding interactions were found to be the most common in the studied surfaces, which could be due to charge transfer occurring on the studied surface. The interactions observed between the donor and acceptor orbitals with transitions for with corresponding stabilization energies 13,994.76 kcal/mol, 13,762.25 kcal/mol, 12,713.99 kcal/mol, 2423.62 kcal/mol and 800.85 kcal/mol respectively. The greatest intermolecular and intramolecular interaction was found in QD-CCC; Donor σ (C 11 -C 12 ) -Acceptor σ *(C 9 -C 10 ) − (85,405.61 kcal/mol) resulting from C-C bonding interaction. In QD-NBS, the lowest noticeable interaction resulted from the interaction between (C 8 -C 30 ) donor and σ*(C 22 -C 25 ) acceptor with an energy value of (800.85 kcal/mol). The major interactions observed in this study arise from the charge transfer between σ and σ* antibonding orbitals of carbon atoms as a result of an increase in electron density within the studied surfaces. The stability order of the examined QDs is as follows: QD-CCC>, QD-NBC >, QD-NBS.

QTAIM analysis
QTAIM is a powerful tool for topology analysis containing the type and structure of bonds and intermolecular interactions. To further study the nature of interaction between the isoniazid drug and the different quantum dots QTAIM theory is employed to analyze the characteristics of the intermolecular hydrogen bond with the presence of critical points. The density of electrons ρ(r), Laplacian of electron density ∇ 2 ρ(r), Lagrangian kinetic energy G(r), Hamiltonian kinetic energy K(r), Energy density H(r) and Bond critical point (BCP) is explored using the quantum theory of atom in molecules [33]. QTAIM aids in interpreting bonding interactions and explicates the chemistry of interactions in simple terms. The significant and highest values for e(r), ∇e(r) G(r), K(r) and H(r) is presented in Table 4.

Adsorption energies
To further evaluate the interactions between the isoniazid drug and the various quantum dots, adsorption energy (E ad ) values were calculated for the optimized structures. The values for adsorption energy were calculated using Eq. (1). The adsorption energy for the studied systems were computed and presented in Table 5. The negative values for adsorption energy indicate higher contacts (attraction) and infer that adsorption process is exothermic, and also the results reflect successful drug-surface interactions. In comparison to NBC, doping the QD with N (NBS) increases the adsorption ability. NBC has adsorption energies of − 24.29, 24.26, and 23.88 kcal/mol, while NBS has adsorption energies of 33.73 and 33.71 kcal/mol. Several computational methods have been used to calculate adsorption energies on various surfaces. For precision and stability, several functionals were utilized in computing adsorption energies for the examined interactions. Adsorption energies were computed, as shown in Table 6, using B3LYP, CAM-B3LYP, GD3BJ, PBE0 & WB97XD/6− 311+G (d,p). The most stable complex is QD_NBS with adsorption energy of − 33.75 kcal/mol at GD3BJ/6− 311+G (d,p), this is due to the dispersion correction in functional which is suitable for predicting weak interactions. Herein, isoniazid interacted with QD_NBS through the different heteroatoms. The findings show that the isoniazid drug interacts successfully with quantum dots (NBC & NBS). Furthermore, the adsorption distance indicates the amount of interaction between the drug and the quantum dots. According to the findings, the adsorption distance between various interactions ranged from 2.817 to 4.246, indicating that the drug and quantum dots interact favorably.

Comparison with other works
Our results for adsorption energy in comparison with other DFT calculations performed by Morteza and Vantaparast show that isoniazid interacts with AlN GQD from both -NH2 and -C=O sites [9]. Interestingly, a comparative study for the adsorption of isoniazid is presented in this session in comparison to our obtained results. Using B3LYP and M062x/6− 31G (d,p) Morteza Vatanparast and Zahra Shariatinia [9] observed an adsorption energy of − 65.88, − 47.29, − 44.43, − 30.61, and − 29.14 kcal/mol respectively for isoniazid on graphene. In addition, it was observed that the adsorption energies on the doped graphene surface are more negative than that of the pure GQD. Hence, doping increases the adsorption ability of surface. El-Mageed et al., reported the adsorption energies of Table 5 Adsorption energies for quantum dot surface and isoniazid drug.    [15]. Adsorption of isoniazid on a C30B15N15 surface shows that isoniazid drug has a greater tendency for adsorption on the QD-NBS in comparison to C30B15N15. Results from literature are in good agreement with that obtained.

Thermodynamic parameters
The enthalpy of a system (H), is the sum of its internal energy and the products of its volume and pressure, this is represented as ΔH = pΔv [33]. Enthalpy is a function for different measures in biological and chemical systems that help to distinguish between a system's products and reactants. When ΔH > 0 the reaction is said to be endothermic and when ΔH < 0 the reaction is said to be the exothermic. In this study, the calculation for enthalpy of reaction for various quantum dots was performed using data attained from the optimized quantum dots using the following equations [34].
where E 0 = Electronic energy; H corr = Thermal correction to enthalpy. In this study, results obtained for enthalpy of a reaction shows that the interaction between isoniazid and QD-NBC and QD-NBS resulted in negative value. QD-NBS has the highest enthalpy of reaction (− 81.22 kcal/mol) and suggest the interaction is highly exothermic due to it negative value. Moreover, the enthalpy values obtained suggest a better interaction between the isoniazid and QD-NBC and QD-NBS.
The reversible function of work performed by a thermodynamic system is calculated using the Gibbs free energy (G) of the system, which is a thermodynamic potential. It expresses the whole of its temperature, entropy and enthalpy product [35]. It's represented as ΔG 0 = ΔH 0 -TΔS 0 , where ΔG 0 = Gibbs free energy, ΔH 0 = change in enthalpy of the system, and TΔS 0 = change in entropy of the system. Δ r G 0 (298k) = Ʃ Ʃ( Ɛ 0 + G corr ) products -Ʃ Ʃ( Ɛ 0 + G corr ) reactants (10) where; Ɛ 0 = Electronic energy; G corr = Thermal correction to free energy. Gibbs free energy (ΔG), is classified into spontaneous and non-spontaneous. High negative value for ΔG is an indication of a thermodynamically favored reaction. The calculated ΔG values in models A and B were slightly negative with values of − 17.22 and − 16.85 kcal/mol, respectively as reported by Gashemi et al. [36]. From our results obtained for ΔG compared to other works, the interactions between the isoniazid and the various quantum dots confirm that the interactions are highly spontaneous and thermodynamically favored as reported in Table 7. In addition, Isoniazid and QD-NBS gave the highest free energy of interactions (− 81.22 kcal/mol) resulting with the highest negative value for ΔG. Therefore, Results obtained for thermodynamic properties is in good agreement with that for adsorption energy and confirms isoniazid drug delivery by quantum dot surface doped with heteroatoms to be thermodynamically favored.

Noncovalent interaction (NCI)
Non-covalent interactions encompass the distinctions of interactions between molecules or within a molecule [37]. It is classified by; electrostatic interactions, van der Waal forces and hydrophobic effects. Non-covalent interaction is of critical importance in chemical and biological interactions and is heavily involved in biological processes in which large molecules binds explicitly to one another [38]. The most common approach to examining noncovalent interactions has been to assign van der Waals interactions (vdW), steric hindrance (SH), and hydrogen bonds (HBs). The results of QTAIM, in the previous section, described the nature of the interactions between isoniazid and quantum dots as non-covalent therefore, it is useful to confirm them by a non-covalent analysis. The two functions RDG and sign (λ 2 ) (r)p(r) are used to define specific areas. Based on second eigenvalue of the electron density Hessian matrix (λ 2 ) and electron density (ρ), sign(λ 2 )ρ < 0 represents an attractive interaction (such as hydrogen bonding); sign(λ 2 )ρ > 0 implies a repulsive interaction (such as steric repulsion); sign(λ 2 )ρ ≈ 0 indicates the presence of van der Wals (vdW) interaction [41]. Non-covalent interactions can be characterized in the region with low electron density and low RDG. The reduced density gradient (RDG) isosurface can be applied to visualization of weak interactions on a blue-green-red scale. RDG isosurface and VMD visualization for studied complexes is shown in Figure 3. RDG functions can be defined as;     Figure 4. In addition, the blue region for isoniazid and QD-NBS S-O shows a hydrogen bond interaction with steric hindrances (Red), this could be as a result of hetero atoms nitrogen and sulfur replacing carbon atoms in the central ring of the quantum dots, and sulfur interacting from the quantum dot to oxygen from the drug. The green region between isoniazid drug and various interactions is the central driving force for isoniazid drug delivery in Figure 4 [9].

Conclusions
Wide-ranging theoretical investigations using DFT method for the interaction of isoniazid drug on NBS, NBC quantum dots was carried out to determine its potential for the delivery of isoniazid. Negative values for adsorption energy confirm surfaces are suitable for drug delivery. However, the highest negative value for adsorption was observed for QD-NBC and QD-NBS. The most stable complex for adsorption was observed for QD-NBC & NBS with GD3BJ/6− 311+G(d,p) level. From the FMO section QD-NBS is the most reactive with small energy gap, both in the isolated and after delivery state. The negative values for enthalpy specify the exothermic nature of the isoniazid and quantum dots interaction. In addition, negative value for Gibbs free energy indicates spontaneous interaction between the isoniazid drug and quantum dots. The results obtained from non-covalent interactions suggest that the interaction between isoniazid and quantum dot NBC, NBS could be used as possible carriers for drug delivery application and is in agreement with the results for QTAIM analysis which revealed also the intermolecular interactions, these results indicate good relationship between the adsorption energy and thermodynamic properties calculated in this study. As a result we can conclude that quantum dots surfaces doped with heteroatoms can deliver isoniazid drugs.

Author contribution statement
Henry O. Edet: Analyzed and interpreted the data; Wrote the paper.